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David B. DavidsonDept. E&E EngineeringUniversity of StellenboschStellenbosch 7600, South Africa(+27) 21 808 4458(+27) 21 808 4981 (Fax)davidson~ing.sun.ac.za (e-mail)

Foreword by the Editor

This column frequently features papers describing variouscomputer codes, and this was indeed one of the original aims of thecolumn. The Internet has made it exceptionally easy to distributesuch software, and the majority of our columns include sites fromwhich to download the software described in the paper. Thisissue's contribution addresses reflector-antenna analysis; in theJune 2005 column, a paper was published on using the sameJacobi-Bessel series method for analyzing reflector antennas, using

MATHCADO- What distinguishes this issue's paper is the use of theinternet to actually run the code, via Java applets within thebrowser.

We thank the authors for their submission. It may well be thefirst submission in this column from South America, and continuesto emphasize the global nature of our profession and the IEEE.

Analysis of Reflector Antennasthrough the World Wide Web

Rafael Rabelo1, Marco Teradal, and Warren Stutzman2

'Antenna Group, Department of Electrical EngineeringUniversity of Brasilia

Brasilia, DF 70919-970 - BrazilE-mail: terada@ene.unb.br

'Antenna Laboratory, Department of Electrical EngineeringVirginia Tech

Blacksburg, VA 24061, USAE-mail: stutzman@vt.edu

Abstract

This article describes the software WebPRAC (Parabolic Reflector Analysis Code for the Web). The Internet version waswritten as a Java applet of PRAC for DOS [1] and PRAC for Windows [2]. PRAC is a user-friendly code designed foranalyzing offset parabolic reflector antennas with high precision and accuracy. It has been extensively used over the pastdecade in teaching (currently, distributed with [3]), research, and industrial development. WebPRAC is intentionally designedfor the Internet, running directly from within the Web browser on all usual operating systems (Windows, Linux, Macintosh,Solanis, etc.).

Keywords: Offset reflector antennas; numerical analysis; physical optics; polarization; antenna radiation patterns; Java;Internet: Bessel functions

IEEE Antennas and Propagation Magazine, Vol. 49, No. 2, April 200711 113

1. Introduction

T he Internet can be deemed the greatest invention of the twenti-eth century, connecting billions of people from different eco-

nomic and social backgrounds. Nowadays, surfing the Web is ascommon as eating, sleeping, working, or talking over a cellularphone (not even considering VoIP?). Therefore, it is logical thatcomputer codes intended for widespread use become a dynamicpart of the Internet.

The Java applet technology [4] (the name stands for smallapplications, although they can be of virtually any size) is one wayto allow users to run codes directly from within their Web brows-ers, without the need for downloading and installation procedures.In the past few years, there have been reports of codes within theareas of antennas and propagation following this pattern, althoughnot necessarily using Java applet technology [5].

This article discusses the implementation in a Java applet ofthe code WebPRAC, written to analyze axisymmetric and offsetparabolic reflector antennas. WebPRAC has been widely used inteaching [3], research, and development, with its accuracy havingbeen validated over the past decade [ 1, 2, 6]. It employs the Jacobi-Bessel series method [1, 2, 7-9] to evaluate the radiation integral,which yields fast processing even when analyzing very large reflec-tors, such as the 100-in-projected-diameter Green Bank RadioTelescope [6]. WebPRAC is a user-friendly code for the Internet,designed to analyze reflector antennas with high precision andaccuracy. Although there are other codes and scripts based on theJacobi-Bessel method (such as [8]), as far as the authors know,none of them is especially tailored for the Internet, as well as forfreely distributed software and operating systems (Linux, Solaris,etc.).

2. The Java Applet Technology

The Java language [4] is widely known as one of the lan-guages of choice for Internet applications. It has been extensivelyused over the past decade, and is based on object-orientedprogramming (OOP), which allows easy maintenance andunderstanding of the code [4]. A major advantage of Java is thatthe same code runs on all the usual operating systems (Windows,Linux, Macintosh, Solaris, etc.), without the need for recompilingthe code. This is possible due to the virtual machine technology,developed and freely distributed by Sun [4] for the users of theaforementioned operating systems.

The virtual machine mimics a processor for which themachine-language instructions are compiled by the Java compiler.A complete development kit (the Java Development Kit or JDK),as well as integrated development environments (such as Netbeans,from which you can write, compile, and test your code), are freelydistributed and have been recently open-sourced [4]. Severaldiscussion forums are also available over the internet.

The applet technology allows the code to be compiled in away such that it can be run directly from within a Web browser,thus avoiding downloading and installing the code. Of course, ifthe code is too large and the Internet connection is too slow, it cantake a while before the code starts running. Java applets currentlyare up to a few megabytes in size, a figure that can increase asInternet connections become faster. WebPRAC is about one mega-

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byte in size. For those familiar with computer languages such as Cor FORTRAN, it is enough to say that once the code is translated toJava, or originally written in Java, a few commands in the headerof the source code instruct the compiler to produce an applet. Thenit is necessary to generate a Web page (index.htm for WebPRAC)with the necessary instructions to display and run the code whenaccessed. In order to run the code online, an Internet server is alsoneeded. The home page for WebPRAC is

http://www.ene.unb.br/-teradalantennas

It is worthy mentioning that the compiled code and Web pagecan also be downloaded and run offline. The aforementionedprocedure only works for Java-enabled browsers, which must berunning on machines where the Java virtual machine plug-in (partof the Java runtime environment, or JRE) has been previouslyinstalled [4]. However, most of today's Web browsers already havethe plug-in installed, and many services use the plug-ins, such asInternet banking.

Finally, we mention that the applet technology is very secure.As a matter of fact, security issues are constantly being addressedand improved by the applet community, in order to safeguard theadvantages of the technology. Applets such as WebPRAC cannothave total access to the user's computer hardware. For example,directly printing and loading/saving files are not allowed. How-ever, it is possible to capture the screen through the "Print Screen"keyboard command, and paste it into another application for print-ing WebPRAC results.

3. Numerical Implementation and Results

The geometry of the offset parabolic reflector antenna isdepicted in Figure 1. Note that the symmetrical reflector is a spe-cial case where H = 0 ( D = Dp ), and is therefore included in the

derivations presented in this work. The Jacobi-Bessel series method[1, 2, 7-91 is employed to solve the radiation integral [9]. Theprocedure consists of expanding part of the kernel of the radiationintegral in a function withf the modified Jacobi polynomials, whichform a complete set of orthogonal functions defined over a disk ofunit diameter [9]. A Fourier series is employed in the circumferen-tial direction, and a complex Taylor series expansion is used in thederivations. After several manipulations, the final result for theelectric field is given by

Figure 1. The geometry of the offset parabolic reflectorantenna.

IEEE Antennas and Propagation Magazine, Vol. 49, No. 2, April 2007

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Figure 3. A screen shot of the computed co-polarized (COPOL)and cross-polarized (XPOL) patterns at 11.25 GHz in the planeorthogonal to the plane of offset (Il-plane).

IEEE Antennas and Propagation Magazine, Vol. 49, No. 2, April 200711 115

E, (i) = j' 0 D2 ejG ejkHu e 4F J'2 ,rejk(D/1'6+~

-]4A 41rR

(w 1)(C .' .': ' , (1)S

Java and implemented as an applet. The software was presented,along a brief overview of the Java-applet technology, includingremarks addressing the Java virtual machine and security issues.WebPRAC is a high-precision reflector analysis code, designed torun directly from within the Web browser on all common plat-forms. It is well suited for teaching, research, and developmentactivities.

with

I C 1 1 2 = ' o n 'm rJ 2 1 fO sin (no') mSo)F s'sd's5. Acknowledgment

This work was partially supported by CNPq (Brazilian(2) National Research Council).

where the primes are used with reference to the source region,x'-=x and y'=-y in Figure 1. The relation P=1u + 'v + w wasused in the derivations, and the index c denotes the components x,y, and z. The function fc (so',q) is the part of the kernel of theradiation integral expanded in terms of the modified Jacobipolynomials, F." (s'), p'=- (D/2)s', and 6,~ is Neumann's number

191].

It is important to note that numerical integration is onlynecessary for the determination of the coefficients C and D. Thecoefficients I are computed from recurrent complex relations inclosed form, which are herein omitted for simplicity [9]. Once thecoefficients C and D are determined, the co-polarization (COPOL)and cross-polarization (XPOL) radiation patterns can be computedat any observation angle without the need of numerical integration.This represents a great advantage over the direct computation ofthe radiation integral [9], which needs to be processed repeatedlyfor each observation point.

The computer screen containing the Web browser andWebPRAC is shown in Figure 2. The same figure lists the defaultinput values. The user has the option of plotting the co-polarizedand cross-polarized patterns, shown in Figure 3, or generating atable with the values. The table can then be used in post-processingroutines for various purposes in Open Office, AMATLAB, MicrosoftExcel, or other programs.

The validation of the WebPRAC results through comparisonwith other codes and with measurements was demonstrated forPRAC for DOS and PRAC for Windows. They were found to bevery accurate [1, 2, 6]. For example, the gain values computed withWe bPRA C and its predecessors (written in Pascal and VisualBasic) agreed up to around six decimal places in dB.

4. Conclusions

This article described the software We bPRA C (ParabolicReflector Analysis Code for the Web). The code was written in

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6. References

1. M. Terada and W. L. Stutzman, "Computer-Aided Design ofReflector Antennas," Microwave Journal, 38, August 1995, pp. 64-73.

2. M. Terada, "Reflector Antennas," in Kai Chang (ed.), WileyEncyclopedia of RF and Microwave Engineering, Volume 5, NewYork, John Wiley and Sons, 2005, pp. 4450-4474.

3. W. L. Stutzman and G. A. Thiele, Antenna Theory and Design,Second Edition, New York, John Wiley & Sons, 1998.

4. http://java.sun.com

5. A. J. Kostaridis, C. G. Biniaris, A. J. Marsh, H. T. Anastassiuand D. 1. Kaklamani, "Integrating Antenna Modeling Codes inWeb-Based Visualization Environments," IEEE Antennas andPropagation Magazine, 45, 4, August 2003, pp. 11-18.

6. M. Terada and W. L. Stutzman, "Computer-Aided Design ofReflector Antennas: The Green Bank Radio Telescope," IEEETransactions on Microwave Theory and Techniques, MTT-46,March 1998, pp. 250-253.

7. Y. Rahmnat-Samii and V. Galindo-Israel, "Shaped ReflectorAntenna Analysis Using the Jacobi-Bessel Series," IEEE Transac-tions on Antennas and Propagation, AP-28, 1980, pp. 425-43 5.

8. Ismatullah and 1. E. Rana, "Implementation of the Jacobi-BesselSeries Method for Radiation Pattern Equations of an Offset Para-bolic Reflector Antenna Using MathCAD," IEEE Antennas andPropagation Magazine, 47, 3, June 2005, pp. 99-104.

9. C. Scott, Modern Methods of Reflector Antenna Design,Norwood, MA, Artech House, 1990. .

IEEE Antennas and Propagation Magazine, Vol. 49, No. 2, April 2007